Regression Analysis – Chi Square Test vs Logistic Regression Results

Question

If I use both chi square test and logistic regression are the result will be the same in terms of P-value and numbers?

Answer 1

The $\chi^2$ test is equivalent to a Score test of nested logistic (or multinomial logistic) regression models: one containing only an intercept and the other containing a categorical predictor variable (with one feature dropped and subsumed by the intercept, the typical way of doing categorical variables in ANOVA). In that sense, the $\chi^2$ test is equivalent to logistic regression, yes.

Most software (by which I mean glm in R) gives Wald-based p-values by default, not Score-based. In that sense, I would regard the answer as no, logistic regression on a categorical variable is not the same as a $\chi^2$ test. If you just look at the values in the software printout, they are unlikely to be derived from the Score test, so they will not have the relationship to the $\chi^2$ test.